I have this exercise of statistics:
The attached table shows the approximate values of the distribution in quintiles of the family income per capita in Chile. Which of the following statements is true?
A) 20% have an income equal to 71 thousand pesos.
B) 40% have an income equal to 118 thousand.
C) 60% have an income higher than 182 thousand pesos.
D) 20% have an income not higher than 71 thousand pesos.
E) 20% have an income greater than 333 thousand pesos.
My development was:
The option $A)$ can't be because the data of the first quintile will be MINOR or EQUAL to quintile 1, i.e. I can not assure you, that all the values under quintile 1 will be equal to 71,000
The option $B)$ Same argument of $A)$
The option $C)$ is false because the $60%$ minimum is $118.000$. So, for this answer to be correct, it should be: Greater than or equal to 118,000
The option $D)$ This must be true, because the values under the first quintile are LESS or EQUAL to the first quintile ( $71000$ )
The option $E)$ Also is false, because between the four quintile that is $80$% and $100$% the values will be GREATER or EQUAL to the fourth quintile. i.e. I can not say that they will be greater.
However, the correct answer should be $ E) $ and I do not understand why, so I am thinking that all my procedure is wrong. Thanks in advance
PS: I have learned that the values below any quintile ($Q_1$ or $Q_2$ $Q_3$ or $Q_4$) will be LESS or EQUAL.
For example in the statistical sample: 1-1-1-1-5-7-8-9-10
The $Q_1$ is $1$, and its position is $2.4$, and also below it there are only numbers equal to it (which are the $1$ repeated)
And also ABOVE any quintile ($Q_1$ or $Q_2$, $Q_3$ or Q_4$) will be GREATER or EQUAL
For example, in the sample: 1-3-4-5-6-7-7-7-7-7-7-7
The $Q_4$ is $7$, and its position is $10.4$, however on it there are values EQUAL to it.
For a sample like this with a large number of possible values we don't worry about how many people have the exact income of the quintile. We can then say that $20\%$ have an income greater than $333.000$ so E is correct. Similarly, $20\%$ have an income less than $71.000$ so D is correct as well. Your point about A and B is correct, you don't have many people with any exact income. C is not correct because $60\%$ have an income below $182.000$ and $40\%$ have an income above.
There are a number of definitions of exactly how to choose the number you report for a quintile when there are ties and when the number of values is not a multiple of $5$. These should not matter for a problem like this.